TITLE: Surprising applications of the theory of games?
QUESTION [8 upvotes]: I am currently studying the applications of games in quantum information theory and related fields and I am aware of its uses in places like model theory and set theory. So I was curious, what are some other somewhat surprising places(somewhat because I am aware of the subjectivity of the term) where games were/are useful tools?

REPLY [2 votes]: Games are used to solve the problem of "full abstraction for the lambda-calculus", which should count as fairly surprising.
Spelling it out a bit: a game can define what a computer program means, satisfying some stringent requirements. The problem is stated such that we need a "meaning" that is not syntactic, i.e. it is quite unlike the source program, and is also expected to be unlike the state of a concrete machine that implements it. And furthermore, it is expected that the distinct objects in the semantics (the "meanings") should exactly match the behaviorally distinct programs. It has turned out that over time, games have been the only kind of solution to that puzzle (I believe). Wikipedia has a brief overview: https://en.wikipedia.org/wiki/Game_semantics